The government should link the salaries of the top public-sector executives to their lowest paid employees to stop the "arms race" in public pay getting out of control, the head of a government inquiry into fair pay says today.

Will Hutton, head of the Work Foundation, gives cautious backing to the idea of a 20:1 maximum pay multiple that would bind public-sector executives' salaries to their employees – essentially capping the top earners to persuade people that public pay is fair and not excessive.

His interim review of fair pay in the public sector, commissioned by the prime minister, reveals that in many parts of the public sector top earners' pay has risen much faster than the average wage. In universities, colleges, local government and hospitals executive pay has risen more rapidly than the lowest paid over the past decade.

Hutton said that the arms race of inflated executive salaries in the private sector was now being replicated in the public sector with civil servants unfairly targeted for perceived unfairness, even though their salaries are still dwarfed by those in the City.

A 20:1 multiple would not force any public-sector organisations to cut executive pay – that ratio stands at 19:1 in top universities, 14:1 in the largest NHS trusts and 10:1 in Whitehall departments – but it would prevent an arms race forcing top salaries up even higher, Hutton's report argues. Organisations with the greatest autonomy from central government – foundation trusts, quangos and universities – have among the highest salaries. and as the government seeks to give more autonomy to schools, hospitals and local government, that upward pressure could increase.

The review found there were about 20,000 public-sector employees earning more than £117,000, while average salaries for executives were £200,000 for heads of universities, £150,000 for NHS Hospital Trust chief executives, £117,000 for local authority chiefs, £170,000 for four-star generals and £160,000 for permanent secretaries in government departments.

Hutton rejects the idea that there is a problem with "fat cats" in the public sector, presenting evidence that public servant salaries are significantly lower than private sector organisations with similar turnovers. The report says: "A media narrative which over-concentrates on public sector fat cats while not offering the same proper scepticism and focus over what is happening at the top of the private sector does not lead to understanding, and can undermine the desirable move to greater transparency over pay."

Hutton said: "Some of the arms race character of top private sector pay determination is also showing signs of reproducing itself in the public sector. On the occasions when the public sector does recruit from the private sector it has to pay significantly more for staff, creating knock-on inflationary pressures."

The report backs the idea of a 20:1 maximum pay multiple, and will now consider whether that level is right and how to measure low earners – options include using a minimum wage or mean salary as a base line to compare executive pay to.

TUC General Secretary Brendan Barber said: "Any moves to tackle pay inequality and the growing divide between top executive pay and the rest of the workforce – whether it's in the public or the private sector – must be welcomed. But this report does not deal with the real issues facing public sector workers. Over the next two years millions of public sector workers face an arbitrary pay-freeze, a real-terms pay cut."